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Heat transfer enhancement by natural convection in a partially porous annular space between two coaxial cylinders saturated by Cu–water nanofluid

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Abstract

The aim of this research is to investigate heat transfer by free convection in an annular, partially porous space between two coaxial cylinders with a permeable interface saturated by (Cu–water) nanofluid. The inner cylinder of the enclosure is kept at a constant hot temperature, while the outer is kept at a constant cold temperature. The base walls are impermeable and insulated. A finite difference-based vorticity-stream function approach is used to solve the nonlinear coupled conservation equations with prescribed boundary conditions, whereas the Successive Over Relaxation algorithm is used to solve the stream function equation. The obtained numerical results in terms of streamlines, isotherms, and heat transfer rate expressed by the Nusselt number are presented to demonstrate the effect of various control parameters, such as the Rayleigh number \(10^{4} \le \mathrm{{Ra}} \le 10^{6}\), Darcy number \(10^{-5} \le \mathrm{{Da}} \le 10^{-2}\), porosity \(0.1\le \epsilon \le 0.9\), nanoparticles concentration \(0.01\le \phi \le 0.05\) and the effective thermal conductivity. They showed that the increase in the Ra number and nanoparticle concentration causes an improvement in thermal energy transmission across the active wall. Also, the increase in the Da number makes the medium more permeable, which means more freedom for nanofluid to move. The results also show a significant effect of the porous layer thickness on the fluid flow pattern and the rate of thermal energy transport. Furthermore, this study demonstrates that there is a critical value of porosity for a given nanoparticle concentration for better heat transfer enhancement. Nonetheless, the purpose of this research could be to better understand the behavior of the nanofluid in this specific configuration, as well as to understand how other characteristics like porosity and porous layer thickness might influence heat transfer and fluid flow characteristics. This knowledge will be useful in a variety of industrial and technological applications where heat transfer efficiency is critical.

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Data Availability Statement

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

Abbreviations

AL:

Aspect ratio

\(R_{i}\) :

Inner radius

\(R_{e}\) :

Outer radius

H :

Cavity height

g :

Gravity acceleration

r, z :

System coordinate

\({\overline{r}},{\overline{z}}\) :

Dimensionless coordinate

\(\textit{T}\) :

Temperature function

\({\overline{T}}\) :

Dimensionless temperature

U, W :

Velocity component

\({\overline{U}},{\overline{W}}\) :

Dimensionless velocity component

K :

Porous medium permeability

Da:

Da number

Pr:

Prandtl number

Ra:

Rayleigh number

\(\mathrm{{Nu}}_{{\mathrm{{{ave}}}}}\) :

Average Nusselt number

\(\mathrm{{Nu}}_{\mathrm{{{loc}}}}\) :

Local Nusselt number

\(C_{p}\) :

Specific capacity

\(\Sigma , \Lambda\) :

Nanofluid constants

\(\beta\) :

Thermal expansion coefficient

\(\lambda\) :

Thermal conductivity

\(\phi\) :

Nanoparticle concentration

\(\mu\) :

Dynamic viscosity

\(\rho\) :

Density

\(\Gamma\) :

Effective viscosity

\(\alpha\) :

Thermal diffusivity

\(\Omega\) :

Vorticity function

\({\overline{\Omega }}\) :

Dimensionless vorticity

\({\overline{\Psi }}\) :

Dimensionless stream function

p :

Porous medium

nf:

Nanofluid

eff:

Effective

c:

Cold

h:

Hot

\(b_{f}\) :

Base fluid

\(n_{p}\) :

Solid nanoparticles

\(\epsilon\) :

Porosity

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  1. Laboratory of Research in Physics and Engineering Sciences, Polydisciplinary faculty, Sultan Moulay Slimane university, Beni Mellal, 23000, Morocco

    Youness Foukhari, Mohamed Sammouda & Mohamed Driouich

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  1. Youness Foukhari
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Correspondence to Youness Foukhari.

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Foukhari, Y., Sammouda, M. & Driouich, M. Heat transfer enhancement by natural convection in a partially porous annular space between two coaxial cylinders saturated by Cu–water nanofluid. Eur. Phys. J. Plus 139, 253 (2024). https://doi.org/10.1140/epjp/s13360-024-04988-5

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